In an adiabatic process:
a. the energy absorbed as heat equals the work done by the systemon its environment
b. the energy absorbed as heat equals the work done by theenvironment on the system
c. the work done by the environment on the system equals the changein internal energy

Answer:

Explanation:

The fundamental frequency of the string  f₀ is expressed as f₀ = V/4L where V is the speed experienced by the string.

[tex]V = \sqrt{\frac{T}{\mu} }[/tex] where T is the tension in the string and  [tex]\mu[/tex] is the density of the string

Given T = 600N and [tex]\mu[/tex] = 0.015 g/cm  = 0.0015kg/m

[tex]V = \sqrt{\frac{600}{0.0015} }\\ \\V = \sqrt{400,000}\\ \\V = 632.46m/s[/tex]

The next is to get the length L of the string. Since the string is stretched and fixed at both ends, 200 cm apart, then the length of the string in metres is 2m.

L = 2m

Substituting the derived values into the formula f₀ = V/2L

f₀ = 632.46/2(2)

f₀ = 632.46/4

f₀ = 158.12 Hertz

Hence the fundamental frequency of the string is 158.12 Hertz

Answer:

Distance= 4 miles

Time = 36.3 seconds

Explanation:

80 mph = 178.95 m/s

90 mph = 201.32 m/s

V = u +at

201.32= 0+a(4.5)

201.32/4.5= a

44.738 m/s² = a

Acceleration of the cop car

= 44.738 m/s²

Distance traveled at 4.5seconds

For the cop car

S= ut + ½at²

S= 0(4.5) + ½*44.738*4.5

S= 100.66 meters

Distance traveled at 4.5seconds

For the speeding car

4.5*178.95=805.275

The cop car will still cover 704.675 +x distance while the speeding car covers for their distance to be equal

X/178.95= (704.675+x)/201.32

X-0.89x= 626.37

0.11x= 626.37

X= 5694.3 meters

The time = 5694.3/178.95

Time =31.8 seconds

So the distance they meet

= 5694.3+805.275

= 6499.575 meters

= 4.0 miles

The Time = 4.5+31.8

Time = 36.3 seconds

Explanation:

The De-Broglie wavelength is given by :

[tex]\lambda=\dfrac{h}{p}[/tex]

h is Planck's constant

p is momentum

In this case, an electron and a proton both moving at nonrelativistic speeds have the same de Broglie wavelength. Mass of electron and proton is different. It means their velocity and energy are different.

Only momentum is the factor that remains same for both particles i.e. momentum.

Answer: R = 394.36ohm

Explanation: In a LR circuit, voltage for a resistor in function of time is given by:

[tex]V(t) = \epsilon. e^{-t.\frac{L}{R} }[/tex]

ε is emf

L is indutance of inductor

R is resistance of resistor

After 4s, emf = 0.8*19, so:

[tex]0.8*19 = 19. e^{-4.\frac{22}{R} }[/tex]

[tex]0.8 = e^{-\frac{88}{R} }[/tex]

[tex]ln(0.8) = ln(e^{-\frac{88}{R} })[/tex]

[tex]ln(0.8) = -\frac{88}{R}[/tex]

[tex]R = -\frac{88}{ln(0.8)}[/tex]

R = 394.36

In this LR circuit, the resistance of the resistor is 394.36ohms.

Answer:

I will explain the concept of magnetic field and how it can be calculated.

Explanation:

The formula for magnetic field at the center of a loop is given as

B = μ[tex]_{o}[/tex]I / 2R

where B is the magnetic field

R is the radius of the loop

I is the current

and μ[tex]_{o}[/tex] is the magnetic permeability of free space which is a constant 4π × [tex]10^{-7}[/tex] newtons/ampere²

If the magnetic field at the center of the loop is 0, then μ[tex]_{o}[/tex]I = 0

I = 0 which means there will be no current flow in the loop.

Answer:

 V = - 3.85 V

Explanation:

The electric potential of a continuous charge distribution is

       V = k ∫ dq / r

to find charge differential let's use the concept of linear density

        λ = dq / dx

       dq = λ dx

the distance from a load element to the point of interest

       x₀ = 23 cm = 0.23 m

       r = √ (x-x₀)² = x - x₀

we substitute

        v = k ∫ λ dx / (x-x₀)

we integrate and evaluate between x = 0 and x = l = 0.10 cm

       V = k λ [ln (x-x₀) - ln (-x₀)]

        V = k λ ln ((x-x₀) / x₀)

let's calculate

         V = 9 10⁹  0.74 10⁻⁹ ln ((0.23 - 0.10) / 0.23)

          V = - 3.85 V

Answer:

A) Workdone = 223.57 N-m

B) 22357 J of energy

C) Number of donuts = 10.7 donuts

Explanation:

A) The work done is calculated from the formula;. Work done = Force × Distance

We are given;

Mass; m = 43 kg

Distance = 0.53 m

Force(weight) = mg = 43 × 9.81

Thus;

Work done = 43 × 9.81 × 0.53

Workdone = 223.57 N-m

B) We are told she does 23 repetitions a day.

Thus, we assume 23% efficiency.

So, Work = Energy

Thus;

At 100% efficiency;

Energy = (223.57/100%) × 23 repetitions = 5142.11 J

Now, since she is only 23% efficient, she will expend; 5142.11/0.23 J = 22357 J of energy to do 5390 J of work.

C) from conversions; 4.18 J = 1 calorie

Thus;

22357 J ÷ 4.18 J/cal = 5348.565 calories

We how many 500 calorie donuts she can eat in a day to supply that energy.

Thus;

Number of donuts = 5348.565 cal ÷ 500 cal /donut

Number of donuts = 10.7 donuts

Answer:

If the wavelength is doubled, the width of the central bright spot on the screen will increase by a factor of 2 (that is, it will also double).

Explanation:

For a single-slit diffraction, diffraction patterns are found at angles θ for which

w sinθ = mλ

where w is the width

λ is wavelength

m is an integer, m = 1,2,3, ....

From the equation, w sinθ = mλ

For the first case, where nothing was changed

w₁ = mλ₁ / sinθ

Now, If the wavelength is doubled, that is, λ₂ = 2λ₁

The equation becomes

w₂ = mλ₂ / sinθ

Then, w₂ = m(2λ₁) / sinθ

w₂ = 2(mλ₁) / sinθ

Recall that, w₁ = mλ₁ / sinθ

Therefore, w₂ = 2w₁

Hence, If the wavelength is doubled, the width of the central bright spot on the screen will increase by a factor of 2 (that is, it will also double).

Explanation:

Mary had 21 plants when she went on vacation.

When she got back, she only had 14 left alive.

We need to find the percent decrease in the number of plants.

Decrease in plants = 21 - 14 = 7

Percent decrease is given by :

[tex]\%=\dfrac{7}{21}\times 100\\\\\%=33.33\%[/tex]

So, there is 33% pf decrease in the number of plants.

Answer:

Explanation:

If the river moves towards the south at 3m/s and the both moves towards the east at 4.0m/s, the speed of the boat relative to me will be the resulting displacement of both velocities of the river and that of the boat. This can be gotten using pythagoras theorem.

Let Vr be the relative speed. According to the theorem;

[tex]V_r^2 = V_s^2 + V_e^2\\\\V_r^2 = 3.0^2 + 4.0^2\\\\V_r^2 = 9+16\\\\V_r^2 = \sqrt{25}\\ \\V_r = 5.0m/s[/tex]

Hence this relative speed is 5.0 m/s

Answer:

[tex]density \: = \frac{mass}{volume} [/tex]

1 / 5.587 is equal to 0.179 kg/m³

Hope it helps:)

Answer:

The answer is

Explanation:

Density of a substance is given by

[tex]Density \: = \frac{mass}{volume} [/tex]

From the

mass = 1 kg

volume = 5.583 m³

Substitute the values into the above formula

We have

[tex]Density \: = \frac{1 \: kg}{5.583 \: {m}^{3} } [/tex]

We have the final answer as

Hope this helps you

Answer:

Δx = 4.68 x 10⁻³ m = 4.68 mm

Explanation:

The distance between the consecutive maxima, in Young's Double Slit Experiment is given bu the following formula:

Δx = λD/d

So, the distance between the eighth order maximum and the fourth order maximum on the screen will be given as:

Δx = 4λD/d

where,

Δx = distance between eighth order maximum and fourth order maximum=?

λ = wavelength = 487 nm = 4.87 x 10⁻⁷ m

d = slit separation = 0.2 mm = 2 x 10⁻⁴ m

D = Distance between slits and screen = 48 cm = 0.48 m

Therefore,

Δx = (4)(4.87 x 10⁻⁷ m)(0.48 m)/(2 x 10⁻⁴ m)

Δx = 4.68 x 10⁻³ m = 4.68 mm

Given that,

A charged particle enters a magnetic field with an angle theta .

If [tex]\theta=90^{\circ}[/tex]

We know that,

If the angle is 90° then the charged particle enters perpendicular to the B.

B is magnetic field.

The charged particle will be follow of the circular path.

If the angle is greater than 0 and less than 90° then the charged particle will be show the helical path.

Hence, This is required answer.

Answer:

Current =,charge / time

Charge = e = 1.6E-19 coulombs

t = T time for 1 revolution  (period)

v = S / T = distance traveled in 1 revolution / time for 1 revolution

T = S / v = 2 pi * 4.76E-10 / 2.43E5 = 1.23E-14

I = Q / T = 1.6E-19 / 1.23E-14 = 1.30E-5

Answer:

10.8rev

Explanation:

Using

Wf²-wf = 2 alpha x theta

0²- 56.36x56.36/ 2(-20.13) x theta

Theta = 68.09 rad

But 68.09/2π

>= 10.8 revolutions

Explanation:

Answer:

The width of Center bright fringe is 10.2mm

Explanation:

Given that if

Y/ L << 1 then

Sin theta will be approx Y/L

So sin theta approx Y/L = lamda/a

Y= a x lambda/a

By substituting

1.9x 10^ -3m x 550*10^-9/ 0.2 x 10^-3m

= 5.2mm

But

Change in y = 2y = 10.4mm

Complete question is;

A force stretches a wire by 0.60 mm. A second wire of the same material has the same cross section and twice the length.

a) How far will it be stretched by the same force?

b) A third wire of the same material has the same length and twice the diameter as the first. How far will it be stretched by the same force?

Answer:

0.15 mm

Explanation:

According to Hooke's Law,

E = Stress(σ)/Strain(ε)

Where E is youngs modulus

Formula for stress is;

Stress(σ) = Force(F)/Area(A)

Formula for strain is;

Strain(ε) = Change in length/original length = (Lf - Li)/Li

We are also told that a second wire of the same material has the same cross section and twice the length.

Thus;

Rearranging Hooke's Law to get the constants on one side, we have;

F/(AE) = ε

Thus from the conditions given;

ε1 = 0.6/Li

ε2 = (Change in length)/(2*Li)

And ε1 = ε2

Thus;

0.6/Li = Change in length/(2*Li)

Li will cancel out and we now have;

Change in length = 2 × 0.6 = 1.2 mm

Finally, we are told A third wire of the same material has the same length and twice the diameter as the first.

Area of a circle;A1 = πd²/4

Now, we are told d is doubled.

Thus, new area of the new circle is;

A2 = π(2d)²/4 = πd²

Rearranging Hooke's Law,we have;

F/A = εE

Since F and E are now constants, we have;

F/E = constant = Aε

Thus;

A1(ε1) = A2(ε2)

A1 = πd²/4

e1 = 0.60/Li

A2 = πd²

e2 = Change in length/Li

Thus;

((πd²/4) × 0.6)/Li = (πd² × Change in length)/ Li

Rearranging, Li and πd² will cancel out to give;

0.6/4 = Change in length

Change in length = 0.15 mm

Answer:

first order date and most recent order date

Explanation:

it was switched. column 5 should be most recent order date because it's 2020 while column 6 should be first order date because it was in 2019

Answer:

Using a process of testing ideas and gathering evidence

Explanation:

Answer:

The resultant vector is [tex]\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j[/tex].

Explanation:

First, each vector is determined in terms of absolute coordinates:

6-meter vector with direction: 30º north of east.

[tex]\vec A = (6\,m)\cdot (\cos30^{\circ} \,i + \sin 30^{\circ}\,j)[/tex]

[tex]\vec A = 5.196\,i + 3\,j[/tex]

4-meter vector with direction: 30º east of north.

[tex]\vec B = (4\,m)\cdot (\cos 60^{\circ}\,i + \sin 60^{\circ}\,j)[/tex]

[tex]\vec B = 2\,i + 3.464\,j[/tex]

The resultant vector is obtaining by sum of components:

[tex]\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j[/tex]

The resultant vector is [tex]\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j[/tex].

Answer:

10m

Explanation:

Since Given frequency f= 1/t

and velocity ν=10 m/s

We know ν=λf

λ= ν/f

​ = 10/1/0.5

=5m

Since both the waves are similar but moves in opposite direction its total wavelength of the wave will be 10 m

Answer:

A) 0.0267 T

B) 0.0263 T

Explanation:

Given that

The number of turns, N = 400

Radius of the wire, r = 6 cm = 0.06 m

Current in the wire, I = 0.25 A

Relative permeability, K(m) = 80

See the attached picture for the calculation

Answer:

the force decreases by a factor of 4

Explanation:

The expression for the law of universal gravitation is

          F = [tex]G \frac{m_1m_2}{r^2}[/tex]

let's call the force Fo for the distance r

          F₀ = [tex]G \frac{m_1m_2}{r^2}[/tex]

They indicate that the distance doubles

          r ’= 2 r

we substitute

          F = [tex]G \frac{m_1m_2}{(r')^2}[/tex]

          F = [tex]G \frac{m_1m_2}{r^2} \ \frac{1}{4}[/tex]

          F = ¼ F₀

consequently the correct answer is that the force decreases by a factor of 4

If the distance between two large masses are doubled, the gravitational force between them weakens by a factor of 4.

Let the initial force be F

Let the initial distance apart be r

Thus, we can obtain the final force as follow:

Initial force (F₁) = F

Initial distance apart (r₁) = r

Final distance apart (r₂) = 2r

F = GM₁M₂ / r²

Fr² = GM₁M₂ (constant)

Thus,

F₁r₁² = F₂r₂²

Fr² = F₂(2r)²

Fr² = F₂4r²

Divide both side by 4r²

F₂ = Fr² /4r²

From the illustration above, we can see that when the distance (r) is doubled, the force (F) is decreased (i.e weakens) by a factor of 4

Learn more: https://brainly.com/question/975812

Explanation:

In Single Slit Experiment:

The width of the central diffraction maximum is inversely proportional to the width of the slit.

Therefore, if we make the slit width smaller, the angle T(representing the angle between the wave ray to a point on the screen and the normal line between the slit and the screen) increases, giving a wider central band.

Answer:

prove that Sin^6 ϴ-cos^6ϴ=(2Sin^2ϴ-1)(cos^2ϴ+sin^4ϴ)

please sove step by step with language it is opt maths question

Answer:

The rms current is 0.3112 A.

Explanation:

Given that,

Suppose, The capacitance is 170 μF and the inductance is 2.94 mH. The resistance in the top branch is 278 Ohms, and in the bottom branch is 151 Ohms. The potential of the power supply is 47 V .

We know that,

When the frequency is very large then the capacitance can be treated as a short circuit and inductance as open circuit.

So,

We need to calculate the rms current

Using formula of current

[tex]I=\dfrac{V}{R}[/tex]

Where, V = voltage

R = resistance

Put the value into the formula

[tex]I=\dfrac{47}{151}[/tex]

[tex]I= 0.3112 \ A[/tex]

Hence, The rms current is 0.3112 A.

Answer:

95.7v

Explanation

Using Faraday's law of electromagnetic induction we know that rate of change in magnetic flux will induce EMF in closed loop

So it is given as

E= Ndစ/dt

E= N BA-0/ deta t

Given that

N = 58turns

B = 1.10T

A = 0.150m^²

Deta t= 0.1s

now we have

E = 58(1.10x0.150)/0.1

= 95.7v

Magnetic flux is decreasing, so the direction of the current will be to aid the decreasing flux $decrease= CLOCKWISE

Explanation:

Answer:

11.2 Ω

Explanation:

The impedance of a circuit is given by;

Z= √R^2 +(XL-XC)^2

Since

Resistance R= 10 Ω

Inductive reactance XL= 12 Ω

Capacitive reactance XC= 7 Ω

Z= √10^2 + (12-7)^2

Z= √100 + 25

Z= √125

Z= 11.2 Ω